Computing zeta functions of Artin-Schreier curves over finite fields. II

DOI10.1016/j.jco.2003.08.009zbMath1119.14018OpenAlexW2075849499MaRDI QIDQ1827573

Daqing Wan, Alan G. B. Lauder

Publication date: 6 August 2004

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:ca50fdb0-542d-4824-b1e7-906cb2d16184

zbMATH Keywords

algorithmhyperelliptic curvefinite fieldzeta functionArtin-Schreier curve

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Exponential sums (11T23) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Computational aspects of algebraic curves (14Q05)

Related Items (6)

Approximating Euler products and class number computation in algebraic function fields ⋮ The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace ⋮ Families of Artin-Schreier curves with Cartier-Manin matrix of constant rank ⋮ Algorithms for modular counting of roots of multivariate polynomials ⋮ A Point Counting Algorithm Using Cohomology with Compact Support ⋮ Counting points on \(C_{ab}\) curves using Monsky-Washnitzer cohomology

Cites Work

• Hyperelliptic cryptosystems
• Computing zeta functions of Kummer curves via multiplicative characters
• On the zeta function of a hypersurface. I
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Géométrie rigide et cohomologie des variétés algébriques de caractéristique $p$
• Exponential Sums on the Complement of a Hypersurface
• Computing Zeta Functions of Artin–schreier Curves over Finite Fields
• On the Rationality of the Zeta Function of an Algebraic Variety
• A p-adic Fixed Point Formula
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